scholarly journals Slow–Fast Dynamics in a Chaotic System with Strongly Asymmetric Memristive Element

2020 ◽  
Vol 30 (08) ◽  
pp. 2050125
Author(s):  
Tom Birkoben ◽  
Moritz Drangmeister ◽  
Finn Zahari ◽  
Serhiy Yanchuk ◽  
Philipp Hövel ◽  
...  
Keyword(s):  
Chaotic System ◽  
Chaotic Behavior ◽  
Base System ◽  
Extended Model ◽  
Memory Element ◽  
Memristive Device ◽  
Double Barrier ◽  
Chua’S Oscillator ◽  
History Of ◽  
Dynamic Bifurcations

We investigate the effect of a memristive element on the dynamics of a chaotic system. For this purpose, the chaotic Chua’s oscillator is extended by a memory element in the form of a double-barrier memristive device. The device consists of [Formula: see text]/Al2O3/Al/Nb layers and exhibits strong analog-type resistive changes depending on the history of the charge flow. In the obtained system we observe strong changes in the dynamics of chaotic oscillations. The otherwise fluctuating amplitudes of Chua’s system are disrupted by transient silent states. Numerical simulations and analysis of the extended model reveal that the underlying dynamics possesses slow–fast properties due to different timescales between the memory element and the base system. Furthermore, the stabilizing and destabilizing dynamic bifurcations are identified that are traversed by the system during its chaotic behavior.

The Tangled Tale of Phase Space

2018 ◽  
Author(s):  
David D. Nolte
Keyword(s):  
Phase Space ◽  
Chaotic Behavior ◽  
Three Body Problem ◽  
Henri Poincaré ◽  
History Of ◽  
The Stability ◽  
Three Body ◽  
Space Phase ◽  
Central Paradigm ◽  
System Phase

This chapter presents the history of the development of the concept of phase space. Phase space is the central visualization tool used today to study complex systems. The chapter describes the origins of phase space with the work of Joseph Liouville and Carl Jacobi that was later refined by Ludwig Boltzmann and Rudolf Clausius in their attempts to define and explain the subtle concept of entropy. The turning point in the history of phase space was when Henri Poincaré used phase space to solve the three-body problem, uncovering chaotic behavior in his quest to answer questions on the stability of the solar system. Phase space was established as the central paradigm of statistical mechanics by JW Gibbs and Paul Ehrenfest.

Dynamics, Synchronization and Electronic Implementations of a New Lorenz-like Chaotic System with Nonhyperbolic Equilibria

2019 ◽  
Vol 29 (14) ◽  
pp. 1950197 ◽  
Author(s):  
P. D. Kamdem Kuate ◽  
Qiang Lai ◽  
Hilaire Fotsin
Keyword(s):  
Chaotic System ◽  
Chaotic Systems ◽  
Lorenz System ◽  
Chaotic Behavior ◽  
Piecewise Linear ◽  
Period Doubling ◽  
Adaptive Synchronization ◽  
The Novel ◽  
Algebraic Equations ◽  
The Lorenz System

The Lorenz system has attracted increasing attention on the issue of its simplification in order to produce the simplest three-dimensional chaotic systems suitable for secure information processing. Meanwhile, Sprott’s work on elegant chaos has revealed a set of 19 chaotic systems all described by simple algebraic equations. This paper presents a new piecewise-linear chaotic system emerging from the simplification of the Lorenz system combined with the elegance of Sprott systems. Unlike the majority, the new system is a non-Shilnikov chaotic system with two nonhyperbolic equilibria. It is multiplier-free, variable-boostable and exclusively based on absolute value and signum nonlinearities. The use of familiar tools such as Lyapunov exponents spectra, bifurcation diagrams, frequency power spectra as well as Poincaré map help to demonstrate its chaotic behavior. The novel system exhibits inverse period doubling bifurcations and multistability. It has only five terms, one bifurcation parameter and a total amplitude controller. These features allow a simple and low cost electronic implementation. The adaptive synchronization of the novel system is investigated and the corresponding electronic circuit is presented to confirm its feasibility.

Impulsive Control and Synchronization of Memristor-Based Chaotic Circuits

2014 ◽  
Vol 24 (12) ◽  
pp. 1450162 ◽  
Author(s):  
Shiju Yang ◽  
Chuandong Li ◽  
Tingwen Huang
Keyword(s):  
Chaotic System ◽  
Impulsive Control ◽  
Chaotic Behavior ◽  
Memory Function ◽  
Sufficient Conditions ◽  
Impulsive System ◽  
Circuit Element ◽  
Chaotic Circuits ◽  
Control And Synchronization ◽  
Passive Circuit

The memristor is a novel nonlinear passive circuit element which has the memory function, and the circuits based on the memristors might exhibit chaotic behavior. In this paper, we revisit a memristor-based chaotic circuit, and then investigate its stabilization and synchronization via impulsive control. By impulsive system theory, some sufficient conditions for the stabilization and synchronization of the memristor-based chaotic system are established. Moreover, an estimation of the upper bound of the impulse interval is proposed under the condition that the parameters of the chaotic system and the impulsive control law are well defined. To show the effectiveness of the theoretical results, numerical simulations are also presented.

scholarly journals Dynamic Analysis and Cryptographic Application of a Sinusoidal-polynomial Composite Chaotic System

2021 ◽  
Author(s):  
Hegui Zhu ◽  
Jiangxia Ge ◽  
Wentao Qi ◽  
Xiangde Zhang ◽  
Xiaoxiong Lu
Keyword(s):  
Image Encryption ◽  
Chaotic System ◽  
Chaotic Behavior ◽  
Initial Conditions ◽  
Encryption Algorithm ◽  
Topological Transitivity ◽  
Detailed Simulation ◽  
Definition Of ◽  
Image Encryption Algorithm ◽  
Sensitivity To Initial Conditions

Abstract Owning to complex properties of ergodicity, non-periodic ability and sensitivity to initial states, chaotic systems are widely used in cryptography. In this paper, we propose a sinusoidal--polynomial composite chaotic system (SPCCS), and prove that it satisfies Devaney's definition of chaos: the sensitivity to initial conditions, topological transitivity and density of periodic points. The experimental results show that the SPCCS has better unpredictability and more complex chaotic behavior than the classical chaotic maps. Furthermore, we provide a new image encryption algorithm combining pixel segmentation operation, block chaotic matrix confusing operation, and pixel diffusion operation with the SPCCS. Detailed simulation results verify effectiveness of the proposed image encryption algorithm.

A Memristor-Based Scroll Chaotic System — Design, Analysis and Circuit Implementation

2014 ◽  
Vol 24 (07) ◽  
pp. 1450099 ◽  
Author(s):  
Huifang Li ◽  
Lidan Wang ◽  
Shukai Duan
Keyword(s):  
System Design ◽  
Chaotic System ◽  
Dynamic Range ◽  
Mathematical Structure ◽  
Maximum Lyapunov Exponent ◽  
Potential Candidate ◽  
Circuit Implementation ◽  
Memory Element ◽  
Triangular Wave ◽  
Analysis Computer

A scroll chaotic system containing a HP memristor model and triangular wave sequence is proposed in this article. Because the memristor is both a nonlinear element and a memory element intrinsically, it is considered a potential candidate to reduce system power consumption and circuit size. A reasonable mathematical structure of triangular wave sequence and the selection of appropriate amplitude, balance point and turning point reduce the dynamic range of signal input caused by the integrator. The proposed system produces a wealth of chaos, just by changing one parameter. Circuit simulations are conducted and the chaotic attractors can be observed. Theoretical analysis, computer simulation and calculation of maximum Lyapunov exponent have been used to research the basic dynamics of this system. The consistency of circuit implementation and computer simulations verifies the effectiveness of the system design.

HUN TUN VERSUS BIG BANG: HOW CLASSICAL CHAOS IMPLIES BOTH "THERMODYNAMICS" AND "CRYODYNAMICS"

2012 ◽  
Vol 22 (02) ◽  
pp. 1230007
Author(s):  
OTTO E. RÖSSLER
Keyword(s):  
Chaotic Behavior ◽  
Big Bang ◽  
Geometric Proof ◽  
Ancient China ◽  
Ancient Greek ◽  
Classical Chaos ◽  
History Of ◽  
Hubble’S Law ◽  
Newtonian Systems ◽  
Point Of Departure

The pre-history of chaos in a rationalist context is taken as a point of departure, starting out with ancient China. The related ancient-Greek "unmixing theory" then leads over to two simple formally 2-body Hamiltonian systems exhibiting chaotic behavior. When the two masses involved are unequal, "pseudoattractors" are formed. Deterministic statistical "thermodynamics" with its dissipative behavior arises when the potential is repulsive. Deterministic statistical "cryodynamics" arises when the potential is attractive. The latter class of Newtonian systems is characterized by "antidissipative" behavior. A geometric proof is sketched in the footsteps of Sinai and Bunimovich. Antidissipative behavior is known empirically from Hubble's law which was so far explained in less fundamental terms. Three experimental examples are proposed.

scholarly journals Morphological Analysis for Three-Dimensional Chaotic Delay Neural Networks

2020 ◽  
Vol 2020 ◽  
pp. 1-6
Author(s):  
Yusong Lu ◽  
Ricai Luo ◽  
Yongfu Zou
Keyword(s):  
Neural Networks ◽  
Chaotic System ◽  
Morphological Analysis ◽  
Chaotic Behavior ◽  
Three Dimensional ◽  
Hopfield Neural Network ◽  
Coefficient Matrix ◽  
Initial Value ◽  
The Neural Networks ◽  
And Control

The study focuses on the chaotic behavior of a three-dimensional Hopfield neural network with time delay. We find the aspecific coefficient matrix and the initial value condition of the system and use MATLAB software to draw its graph. The result shows that their shape is very similar to the figure of Roslerʼs chaotic system. Furthermore, we analyzed the divergence, the eigenvalue of the Jacobian matrix for the equilibrium point, and the Lyapunov exponent of the system. These properties prove that the system does have chaotic behavior. This result not only confirms that there is chaos in the neural networks but also that the chaotic characteristics of the system are very similar to those of Roslerʼs chaotic system under certain conditions. This discovery provides useful information that can be applied to other aspects of chaotic Hopfield neural networks, such as chaotic synchronization and control.

‘The Pots on Our Roads’

2014 ◽  
Vol 7 (1) ◽  
pp. 63-88
Author(s):  
Gerald Chikozho Mazarire ◽  
Sandra Swart
Keyword(s):  
Chaotic System ◽  
The State ◽  
City Council ◽  
The Self ◽  
Traffic Police ◽  
Regulatory Instruments ◽  
History Of ◽  
Vehicle Fleet ◽  
The City

This article explores the role of the ‘diaspora fleet’ in Harare’s urban commuter system. Imported vehicles in the form of haulage trucks and commuter buses were one of the popular and visible forms of diasporic investment over Zimbabwe’s difficult decade spanning from 2000 to about 2010. The article argues that this diaspora fleet occupies a significant place in the history of commuting in Harare. Diasporic investment introduced a cocktail of European vehicles that quickly became ramshackle and ended up discarded in scrap heaps around the city. These imports and the businesses based on them destroyed the self-regulatory framework existing in the commuting business. This disruption was facilitated by the retreat or undermining of the state and city council regulatory instruments, which in turn created a role for middlemen, who manoeuvred to perpetuate a new and chaotic system known as ‘mshika-shika [faster-faster]’, based on a culture of irresponsible competitive gambling. This chaotic system remains in place today to the chagrin of city council planners and traffic police. Its origins, we argue, lie in the cultures and practices introduced by the diasporan vehicle fleet.

scholarly journals S-Box Based Image Encryption Application Using a Chaotic System without Equilibrium

2019 ◽  
Vol 9 (4) ◽  
pp. 781 ◽  
Author(s):  
Xiong Wang ◽  
Ünal Çavuşoğlu ◽  
Sezgin Kacar ◽  
Akif Akgul ◽  
Viet-Thanh Pham ◽  
...  
Keyword(s):  
Image Encryption ◽  
Chaotic System ◽  
Chaotic Systems ◽  
Electronic Circuit ◽  
Chaotic Behavior ◽  
Encryption Algorithm ◽  
Phase Portraits ◽  
Hidden Attractors ◽  
New Chaotic System ◽  
Image Encryption Algorithm

Chaotic systems without equilibrium are of interest because they are the systems with hidden attractors. A nonequilibrium system with chaos is introduced in this work. Chaotic behavior of the system is verified by phase portraits, Lyapunov exponents, and entropy. We have implemented a real electronic circuit of the system and reported experimental results. By using this new chaotic system, we have constructed S-boxes which are applied to propose a novel image encryption algorithm. In the designed encryption algorithm, three S-boxes with strong cryptographic properties are used for the sub-byte operation. Particularly, the S-box for the sub-byte process is selected randomly. In addition, performance analyses of S-boxes and security analyses of the encryption processes have been presented.

Seven Dimension Chaotic System and its Circuit Implementation

2012 ◽  
Vol 588-589 ◽  
pp. 1251-1254 ◽  
Author(s):  
Jian Liang Zhu ◽  
Chun Yu Yu
Keyword(s):  
Chaotic System ◽  
Chaotic Behavior ◽  
Circuit Simulation ◽  
System Simulation ◽  
Chaotic Signal ◽  
Chaotic Attractors ◽  
Signal Source ◽  
Circuit Implementation ◽  
Practical Application ◽  
Signal Encryption

In order to generate more complex chaotic attractors, a seven-dimensional chaotic system is constructed, and relevant chaotic attractors can be obtained by Matlab numerical simulation. Lyapunov exponents validate that the system is chaotic. Implementation circuit of this system is designed, and circuit simulation can be done by using Multisim. Circuit simulation result is identical to system simulation completely. Chaotic behavior of the system is proved farther. A new chaotic signal source is provided for practical application based on chaos such as secrecy communication and signal encryption fields.

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